You forgot a $ in the echo… No matter, it's still readable.
So, okay, what I see is that both the flat-file /etc/resolv.conf and its backup are filled with AirDNS servers, so it doesn't matter whether VPN is on or off, you will not get DNS back using Eddie.
Meanwhile, the resolv.conf.eddie containing the stub resolver (and ultimately the file that will make DNS work again) is from… April.
The fix is thus, after ensuring Eddie is shut down, to remove the current resolv.conf and backup, then renaming the .eddie backup to resolv.conf.
$ rm /etc/resolv{.conf,.conf.eddievpn} && mv /etc/resolv.conf.eddie /etc/resolv.conf
.